We investigate the growth of a pattern of liquid crests emerging in a layer of magnetic liquid when subjected to a magnetic field oriented normally to the fluid surface. After a steplike increase of the magnetic field, the temporal evolution of the pattern amplitude is measured by means of a Hall-sensor array. The extracted growth rate is compared with predictions from linear stability analysis by taking into account the proper nonlinear magnetization curve M (H). The remaining discrepancy can be resolved by numerical calculations via the finite-element method. By starting with a finite surface perturbation, it can reproduce the temporal evolution of the pattern amplitude and the growth rate. The investigations are performed for two magnetic liquids, one with low and one with high viscosity.

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field, the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic Hall sensors and compared with theoretical predictions.

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We investigate the growth of a pattern of liquid crests emerging in a layer of magnetic liquid when subjected to a magnetic field oriented normally to the fluid surface. After a step like increase of the magnetic field, the temporal evolution of the pattern amplitude is measured by means of a Hall-sensor array. The extracted growth rate is compared with predictions from linear stability analysis by taking into account the nonlinear magnetization curve M (H). The remaining discrepancy can be resolved by numerical calculations via the finite element method. By starting with a finite surface perturbation it can reproduce the temporal evolution of the pattern amplitude and the growth rate. "In the beginning was the word, . . . " [1], which reads in the greek original Ò ÖÕ Ò Ð Ó , . . . . The word Ð Ó , however, has a plethora of different meanings, including also "way, manner" which is "modus" in latin, "mode" in english. We may therefore translate John, 1.1: "In the beginning was the mode, . . . ", and indeed at the beginning of an evolving pattern stands an unstable mode [2]. As long as the amplitude of the mode is small, its wave number and growth rate can be calculated by linear stability analysis. In this way the early stage of pattern formation has been investigated in many different systems [2]. In the following we examine the growth of the Rosensweig or normal field instability [3]. It is observed in a layer of magnetic fluid [4], when a critical value B c of the vertical magnetic induction is surpassed. For a sudden increase of the magnetic induction B the growth rate of the fastest growing modeω 2,m was recently calculated in detail [5,6] to follow the equation(1) HereB = (B − B c )/B c denotes the scaled overcritical induction, and c 1 = 1.24 and c 2 = 0.94 the calculated parameters taking into account the measured nonlinear magnetization curve M (H) of the fluid. In the following we report an experimental and numerical test of those predictions.In order to measure the temporal evolution of the growing amplitudes of the surface pattern we utilize a linear array of Hall sensors [7], mounted beneath the bottom of the vessel. Details of the experimental setup and the method of measuring can be found in Ref. [6]. On the basis of the time recorded magnetic profiles, we determine the amplitude from the root-mean-square

The technique of photoluminescence (PL) studies based on intense picosecond excitation of electron–hole pairs is applied to investigate the electron energy structure including the positions of high-lying excited levels in stepped quantum wells (QWs). The spectra of PL in regimes of spontaneous and stimulated emission are studied under different excitation levels and light polarizations. Of special interest are intense photoluminescence signals from excited subbands. The feasibility of a e3–e2 intersubband population inversion in stepped QWs is demonstrated and the influence of Auger recombination was examined.